Estatística Básica

Correlação

Wlademir Prates

Como saber o quanto uma variável anda junto com outra?

Para variáveis numéricas, usamos o coeficiente de correlação
- Indica tanto a direção quanto a força da relação (varia de -1 a 1).

Matriz de correlação

cor(mtcars)

            mpg        cyl       disp         hp        drat         wt
mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684  0.68117191 -0.8676594
cyl  -0.8521620  1.0000000  0.9020329  0.8324475 -0.69993811  0.7824958
disp -0.8475514  0.9020329  1.0000000  0.7909486 -0.71021393  0.8879799
hp   -0.7761684  0.8324475  0.7909486  1.0000000 -0.44875912  0.6587479
drat  0.6811719 -0.6999381 -0.7102139 -0.4487591  1.00000000 -0.7124406
wt   -0.8676594  0.7824958  0.8879799  0.6587479 -0.71244065  1.0000000
qsec  0.4186840 -0.5912421 -0.4336979 -0.7082234  0.09120476 -0.1747159
vs    0.6640389 -0.8108118 -0.7104159 -0.7230967  0.44027846 -0.5549157
am    0.5998324 -0.5226070 -0.5912270 -0.2432043  0.71271113 -0.6924953
gear  0.4802848 -0.4926866 -0.5555692 -0.1257043  0.69961013 -0.5832870
carb -0.5509251  0.5269883  0.3949769  0.7498125 -0.09078980  0.4276059
            qsec         vs          am       gear        carb
mpg   0.41868403  0.6640389  0.59983243  0.4802848 -0.55092507
cyl  -0.59124207 -0.8108118 -0.52260705 -0.4926866  0.52698829
disp -0.43369788 -0.7104159 -0.59122704 -0.5555692  0.39497686
hp   -0.70822339 -0.7230967 -0.24320426 -0.1257043  0.74981247
drat  0.09120476  0.4402785  0.71271113  0.6996101 -0.09078980
wt   -0.17471588 -0.5549157 -0.69249526 -0.5832870  0.42760594
qsec  1.00000000  0.7445354 -0.22986086 -0.2126822 -0.65624923
vs    0.74453544  1.0000000  0.16834512  0.2060233 -0.56960714
am   -0.22986086  0.1683451  1.00000000  0.7940588  0.05753435
gear -0.21268223  0.2060233  0.79405876  1.0000000  0.27407284
carb -0.65624923 -0.5696071  0.05753435  0.2740728  1.00000000

Mapa de calor (heatmap) - Código

library(echarts4r)
cor_chart <- cor(mtcars) |>
  e_charts() |>
  e_correlations(
    order = "hclust",
    visual_map = FALSE
  ) |>
  e_visual_map(
    min = -1,
    max = 1
  ) |>
  e_tooltip()

Mapa de calor (heatmap)

Mantendo apenas uma diagonal

library(rstatix)
replace_upper_triangle(cor(mtcars), by = NA, diagonal = TRUE)

   rowname        mpg        cyl       disp         hp        drat         wt
1      mpg  1.0000000         NA         NA         NA          NA         NA
2      cyl -0.8521620  1.0000000         NA         NA          NA         NA
3     disp -0.8475514  0.9020329  1.0000000         NA          NA         NA
4       hp -0.7761684  0.8324475  0.7909486  1.0000000          NA         NA
5     drat  0.6811719 -0.6999381 -0.7102139 -0.4487591  1.00000000         NA
6       wt -0.8676594  0.7824958  0.8879799  0.6587479 -0.71244065  1.0000000
7     qsec  0.4186840 -0.5912421 -0.4336979 -0.7082234  0.09120476 -0.1747159
8       vs  0.6640389 -0.8108118 -0.7104159 -0.7230967  0.44027846 -0.5549157
9       am  0.5998324 -0.5226070 -0.5912270 -0.2432043  0.71271113 -0.6924953
10    gear  0.4802848 -0.4926866 -0.5555692 -0.1257043  0.69961013 -0.5832870
11    carb -0.5509251  0.5269883  0.3949769  0.7498125 -0.09078980  0.4276059
         qsec         vs         am      gear carb
1          NA         NA         NA        NA   NA
2          NA         NA         NA        NA   NA
3          NA         NA         NA        NA   NA
4          NA         NA         NA        NA   NA
5          NA         NA         NA        NA   NA
6          NA         NA         NA        NA   NA
7   1.0000000         NA         NA        NA   NA
8   0.7445354  1.0000000         NA        NA   NA
9  -0.2298609  0.1683451 1.00000000        NA   NA
10 -0.2126822  0.2060233 0.79405876 1.0000000   NA
11 -0.6562492 -0.5696071 0.05753435 0.2740728    1